Question

Exercise 2

The following two-way table presents data on the opinion of 259 adults about astrology. There are two variables: ``Opinion" with 2 categories (Not-scientific and Sort-of-scientific), and ``Degree held" with 2 categories (Junior-College and Bachelor). The numbers in the table are the counts of adults in each level of Opinion by each level of Degree.

Degree	Opinion
	Not scientific	Sort of scientific
Junior College	44	31
Bachelor	122	62

We want to know whether the variables ``Opinion" and ``Degree" are significantly related, or not. Please answer the following questions underneath each question.

1. Which test is appropriate to investigate the relationship between Opinion and Degree ?

Answer:

2. Conduct the four steps of this test

(for step 1, write your answers in the table below)

Answer:

Step 1:

Degree	Opinion
	Not scientific	Sort of scientific
Junior College
Bachelor

Step 2:

Step 3:

Step 4:

3. State your conclusion in the context of this example

Answer 1

Assuming the = level of significance to be 5%

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Opinion and Degree are independent Ha​: The two variables - Opinion and Degree are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1, so the critical value is 3.8415. Then the rejection region for this test becomes R={χ2:χ2>3.8415}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>1.3506)=0.2452 (6)The decision about the null hypothesis Since it is observed that χ2=1.3506<χ2_c​rit=3.8415, it is then concluded that the null hypothesis is NOT rejected. (7)Conclusion It is concluded that the null hypothesis Ho is NOT rejected. Therefore, there is NOT enough evidence to claim that the two variables - Opinion and Degree are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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